test/verify/yukicoder-1826.test.cpp

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• Last update: 2024-07-28 19:56:12+09:00
• Problem: https://yukicoder.me/problems/no/1826

Depends on

• Abstract 2D Binary Indexed Tree Compressed(抽象化2次元座圧BIT) (structure/others/abstract-2d-binary-indexed-tree-compressed.hpp)
• Abstract Binary Indexed Tree(抽象化BIT) (structure/others/abstract-binary-indexed-tree.hpp)
• template/template.hpp

Code

// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/1826

#include "../../template/template.hpp"

#include "../../structure/others/abstract-2d-binary-indexed-tree-compressed.hpp"

int main() {
  int N;
  cin >> N;
  vector< tuple< int, int, int > > ds;
  ds.reserve(N + 1);
  for(int i = 0; i < N; i++) {
    int t, x, v;
    cin >> t >> x >> v;
    ds.emplace_back(t, x, v);
  }
  ds.emplace_back(0, 0, 0);
  sort(begin(ds), end(ds));
  vector< int64 > dp(ds.size(), -infll);
  dp[0] = 0;
  vector< int > l, r;
  vector< pair< int, int > > m;
  l.reserve(N + 1);
  r.reserve(N + 1);
  m.reserve(N + 1);
  int ptr = 0;
  for(auto&[t, x, v]: ds) {
    l.emplace_back(t + x);
    r.emplace_back(t - x);
    m.emplace_back(x, ptr++);
  }
  sort(begin(l), end(l));
  l.erase(unique(begin(l), end(l)), end(l));
  sort(begin(r), end(r));
  r.erase(unique(begin(r), end(r)), end(r));
  sort(begin(m), end(m));
  vector< int > ldx(ds.size()), rdx(ds.size()), mdx(ds.size());
  for(int i = 0; i < (int) ds.size(); i++) {
    auto[t, x, v]=ds[i];
    ldx[i] = lower_bound(begin(l), end(l), t + x) - begin(l);
    rdx[i] = lower_bound(begin(r), end(r), t - x) - begin(r);
    mdx[i] = lower_bound(begin(m), end(m), make_pair(x, i)) - begin(m);
  }
  auto f = [](int64 a, int64 b) { return max(a, b); };
  // みんなの2D segment tree

  vector< int > ladx(m.size()), radx(m.size());
  for(int i = 0; i < (int) ds.size(); i++) {
    ladx[m.size() - mdx[i] - 1] = ldx[i];
    radx[mdx[i]] = rdx[i];
  }
  auto lseg = get_abstract_2d_binary_indexed_tree_compressed(ladx, f, -infll);
  auto rseg = get_abstract_2d_binary_indexed_tree_compressed(radx, f, -infll);
  vector< int > ord(ds.size());
  lseg.apply(m.size() - mdx[0] - 1, 0);
  rseg.apply(mdx[0], 0);
  int64 ret = 0;
  for(int i = 1; i < (int) ds.size(); i++) {
    auto[t2, x2, v2] = ds[i];
    auto v = max(lseg.prod(m.size() - mdx[i], ldx[i] + 1), rseg.prod(mdx[i], rdx[i] + 1));
    v += v2;
    if(v >= 0) {
      chmax(ret, v);
      lseg.apply(m.size() - mdx[i] - 1, v);
      rseg.apply(mdx[i], v);
    }
  }
  cout << ret << "\n";
}

#line 1 "test/verify/yukicoder-1826.test.cpp"
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/1826

#line 1 "template/template.hpp"
#include <bits/stdc++.h>
#if __has_include(<atcoder/all>)
#include <atcoder/all>
#endif

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v) is >> in;
  return is;
}

template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64>
vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t) fill_v(e, v);
}

template <typename F>
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(std::forward<F>(f)) {}

  template <typename... Args>
  decltype(auto) operator()(Args &&...args) const {
    return F::operator()(*this, std::forward<Args>(args)...);
  }
};

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{std::forward<F>(f)};
}
#line 4 "test/verify/yukicoder-1826.test.cpp"

#line 1 "structure/others/abstract-binary-indexed-tree.hpp"
/**
 * @brief Abstract Binary Indexed Tree(抽象化BIT)
 */
template <typename T, typename F>
struct AbstractBinaryIndexedTree {
 private:
  int n;
  vector<T> data;
  const F f;
  const T e;

 public:
  AbstractBinaryIndexedTree() = default;

  explicit AbstractBinaryIndexedTree(int n, const F f, const T &e)
      : n(n), f(f), e(e) {
    data.assign(n + 1, e);
  }

  explicit AbstractBinaryIndexedTree(const vector<T> &v, const F f, const T &e)
      : AbstractBinaryIndexedTree((int)v.size(), f, e) {
    build(v);
  }

  void build(const vector<T> &v) {
    assert(n == (int)v.size());
    for (int i = 1; i <= n; i++) data[i] = v[i - 1];
    for (int i = 1; i <= n; i++) {
      int j = i + (i & -i);
      if (j <= n) data[j] = f(data[j], data[i]);
    }
  }

  void apply(int k, const T &x) {
    for (++k; k <= n; k += k & -k) data[k] = f(data[k], x);
  }

  T prod(int r) const {
    T ret{e};
    for (; r > 0; r -= r & -r) ret = f(ret, data[r]);
    return ret;
  }
};

template <typename T, typename F>
AbstractBinaryIndexedTree<T, F> get_abstract_binary_indexed_tree(int n,
                                                                 const F &f,
                                                                 const T &e) {
  return AbstractBinaryIndexedTree{n, f, e};
}

template <typename T, typename F>
AbstractBinaryIndexedTree<T, F> get_abstract_binary_indexed_tree(
    const vector<T> &v, const F &f, const T &e) {
  return AbstractBinaryIndexedTree{v, f, e};
}
#line 2 "structure/others/abstract-2d-binary-indexed-tree-compressed.hpp"

/**
 * @brief Abstract 2D Binary Indexed Tree Compressed(抽象化2次元座圧BIT)
 */
template <typename T, typename F>
struct Abstract2DBinaryIndexedTreeCompressed {
 private:
  int n;
  vector<AbstractBinaryIndexedTree<T, F> > data;
  const F f;
  const T e;
  vector<int> hs;
  vector<vector<int> > beet;

 public:
  Abstract2DBinaryIndexedTreeCompressed(const vector<int> &hs, const F f,
                                        const T &e)
      : n((int)hs.size()), hs(hs), f(f), e(e) {
    vector<int> ord(n);
    iota(begin(ord), end(ord), 0);
    sort(begin(ord), end(ord), [&](int a, int b) { return hs[a] < hs[b]; });
    beet.resize(n + 1);
    for (auto &&i : ord) {
      for (int k = i + 1; k <= n; k += k & -k) {
        beet[k].emplace_back(hs[i]);
      }
    }
    data.reserve(n + 1);
    for (int k = 0; k <= n; k++) {
      beet[k].erase(unique(begin(beet[k]), end(beet[k])), end(beet[k]));
      data.emplace_back((int)beet[k].size(), f, e);
    }
  }

  void apply(int k1, const T &x) {
    int k2 = hs[k1];
    for (++k1; k1 <= n; k1 += k1 & -k1) {
      int p = lower_bound(begin(beet[k1]), end(beet[k1]), k2) - begin(beet[k1]);
      data[k1].apply(p, x);
    }
  }

  T prod(int r1, int r2) const {
    T ret{e};
    for (; r1 > 0; r1 -= r1 & -r1) {
      int p = lower_bound(begin(beet[r1]), end(beet[r1]), r2) - begin(beet[r1]);
      ret = f(ret, data[r1].prod(p));
    }
    return ret;
  }
};

template <typename T, typename F>
Abstract2DBinaryIndexedTreeCompressed<T, F>
get_abstract_2d_binary_indexed_tree_compressed(const vector<int> &hs,
                                               const F &f, const T &e) {
  return Abstract2DBinaryIndexedTreeCompressed{hs, f, e};
}
#line 6 "test/verify/yukicoder-1826.test.cpp"

int main() {
  int N;
  cin >> N;
  vector< tuple< int, int, int > > ds;
  ds.reserve(N + 1);
  for(int i = 0; i < N; i++) {
    int t, x, v;
    cin >> t >> x >> v;
    ds.emplace_back(t, x, v);
  }
  ds.emplace_back(0, 0, 0);
  sort(begin(ds), end(ds));
  vector< int64 > dp(ds.size(), -infll);
  dp[0] = 0;
  vector< int > l, r;
  vector< pair< int, int > > m;
  l.reserve(N + 1);
  r.reserve(N + 1);
  m.reserve(N + 1);
  int ptr = 0;
  for(auto&[t, x, v]: ds) {
    l.emplace_back(t + x);
    r.emplace_back(t - x);
    m.emplace_back(x, ptr++);
  }
  sort(begin(l), end(l));
  l.erase(unique(begin(l), end(l)), end(l));
  sort(begin(r), end(r));
  r.erase(unique(begin(r), end(r)), end(r));
  sort(begin(m), end(m));
  vector< int > ldx(ds.size()), rdx(ds.size()), mdx(ds.size());
  for(int i = 0; i < (int) ds.size(); i++) {
    auto[t, x, v]=ds[i];
    ldx[i] = lower_bound(begin(l), end(l), t + x) - begin(l);
    rdx[i] = lower_bound(begin(r), end(r), t - x) - begin(r);
    mdx[i] = lower_bound(begin(m), end(m), make_pair(x, i)) - begin(m);
  }
  auto f = [](int64 a, int64 b) { return max(a, b); };
  // みんなの2D segment tree

  vector< int > ladx(m.size()), radx(m.size());
  for(int i = 0; i < (int) ds.size(); i++) {
    ladx[m.size() - mdx[i] - 1] = ldx[i];
    radx[mdx[i]] = rdx[i];
  }
  auto lseg = get_abstract_2d_binary_indexed_tree_compressed(ladx, f, -infll);
  auto rseg = get_abstract_2d_binary_indexed_tree_compressed(radx, f, -infll);
  vector< int > ord(ds.size());
  lseg.apply(m.size() - mdx[0] - 1, 0);
  rseg.apply(mdx[0], 0);
  int64 ret = 0;
  for(int i = 1; i < (int) ds.size(); i++) {
    auto[t2, x2, v2] = ds[i];
    auto v = max(lseg.prod(m.size() - mdx[i], ldx[i] + 1), rseg.prod(mdx[i], rdx[i] + 1));
    v += v2;
    if(v >= 0) {
      chmax(ret, v);
      lseg.apply(m.size() - mdx[i] - 1, v);
      rseg.apply(mdx[i], v);
    }
  }
  cout << ret << "\n";
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	00_middle00	AC	6 ms	4 MB
g++	00_middle01	AC	7 ms	4 MB
g++	00_middle02	AC	7 ms	4 MB
g++	00_middle03	AC	8 ms	4 MB
g++	00_middle04	AC	6 ms	4 MB
g++	01_rnd00	AC	285 ms	43 MB
g++	01_rnd01	AC	522 ms	71 MB
g++	01_rnd02	AC	326 ms	50 MB
g++	01_rnd03	AC	29 ms	8 MB
g++	01_rnd04	AC	485 ms	68 MB
g++	01_rnd05	AC	303 ms	47 MB
g++	01_rnd06	AC	297 ms	46 MB
g++	01_rnd07	AC	103 ms	20 MB
g++	01_rnd08	AC	48 ms	11 MB
g++	01_rnd09	AC	76 ms	17 MB
g++	02_largest00	AC	840 ms	105 MB
g++	02_largest01	AC	829 ms	105 MB
g++	02_largest02	AC	841 ms	105 MB
g++	02_largest03	AC	857 ms	105 MB
g++	02_largest04	AC	847 ms	105 MB
g++	02_largest05	AC	838 ms	105 MB
g++	02_largest06	AC	835 ms	105 MB
g++	02_largest07	AC	834 ms	105 MB
g++	02_largest08	AC	851 ms	105 MB
g++	02_largest09	AC	844 ms	105 MB
g++	03_small00	AC	6 ms	3 MB
g++	03_small01	AC	5 ms	3 MB
g++	03_small02	AC	5 ms	3 MB
g++	03_small03	AC	5 ms	3 MB
g++	03_small04	AC	5 ms	3 MB
g++	04_zero00	AC	123 ms	25 MB
g++	04_zero01	AC	272 ms	47 MB
g++	05_many00	AC	155 ms	24 MB
g++	05_many01	AC	688 ms	73 MB
g++	05_many02	AC	526 ms	61 MB
g++	05_many03	AC	93 ms	17 MB
g++	05_many04	AC	689 ms	72 MB
g++	06_all00	AC	212 ms	57 MB
g++	06_all01	AC	154 ms	41 MB
g++	07_line00	AC	393 ms	67 MB
g++	07_line01	AC	467 ms	84 MB
g++	07_line02	AC	89 ms	20 MB
g++	07_line03	AC	15 ms	5 MB
g++	08_sample00	AC	6 ms	3 MB
g++	08_sample01	AC	5 ms	3 MB
g++	08_sample02	AC	5 ms	3 MB
clang++	00_middle00	AC	6 ms	4 MB
clang++	00_middle01	AC	6 ms	4 MB
clang++	00_middle02	AC	7 ms	4 MB
clang++	00_middle03	AC	8 ms	4 MB
clang++	00_middle04	AC	6 ms	4 MB
clang++	01_rnd00	AC	318 ms	43 MB
clang++	01_rnd01	AC	639 ms	71 MB
clang++	01_rnd02	AC	368 ms	50 MB
clang++	01_rnd03	AC	29 ms	8 MB
clang++	01_rnd04	AC	560 ms	68 MB
clang++	01_rnd05	AC	337 ms	47 MB
clang++	01_rnd06	AC	337 ms	46 MB
clang++	01_rnd07	AC	108 ms	20 MB
clang++	01_rnd08	AC	48 ms	12 MB
clang++	01_rnd09	AC	78 ms	17 MB
clang++	02_largest00	AC	1078 ms	105 MB
clang++	02_largest01	AC	1048 ms	105 MB
clang++	02_largest02	AC	1095 ms	105 MB
clang++	02_largest03	AC	1114 ms	105 MB
clang++	02_largest04	AC	1096 ms	105 MB
clang++	02_largest05	AC	1059 ms	105 MB
clang++	02_largest06	AC	1029 ms	105 MB
clang++	02_largest07	AC	1072 ms	105 MB
clang++	02_largest08	AC	1098 ms	105 MB
clang++	02_largest09	AC	1103 ms	105 MB
clang++	03_small00	AC	6 ms	3 MB
clang++	03_small01	AC	5 ms	3 MB
clang++	03_small02	AC	5 ms	3 MB
clang++	03_small03	AC	5 ms	3 MB
clang++	03_small04	AC	5 ms	3 MB
clang++	04_zero00	AC	137 ms	25 MB
clang++	04_zero01	AC	299 ms	47 MB
clang++	05_many00	AC	162 ms	24 MB
clang++	05_many01	AC	757 ms	73 MB
clang++	05_many02	AC	557 ms	61 MB
clang++	05_many03	AC	93 ms	17 MB
clang++	05_many04	AC	820 ms	72 MB
clang++	06_all00	AC	241 ms	57 MB
clang++	06_all01	AC	170 ms	41 MB
clang++	07_line00	AC	450 ms	67 MB
clang++	07_line01	AC	559 ms	84 MB
clang++	07_line02	AC	94 ms	20 MB
clang++	07_line03	AC	15 ms	5 MB
clang++	08_sample00	AC	5 ms	3 MB
clang++	08_sample01	AC	5 ms	3 MB
clang++	08_sample02	AC	5 ms	3 MB

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